Aspiration level approach to solve matrix games with I-fuzzy goals and I-fuzzy pay-offs

Abstract

The objective of this paper is to develop a new solution methodology for matrix games, in which goals are viewed as intuitionistic fuzzy sets (IFSs) and the elements of the pay-off matrix are represented by triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, a suitable ranking function is defined to establish an order relation between two TIFNs, and the concept of intuitionistic fuzzy (I-fuzzy) inequalities is interpreted. Utilizing these inequality relations and ranking functions, a pair of linear programming models is derived from a pair of auxiliary intuitionistic fuzzy programming models. Based on the aspiration levels, this pair of linear programming models is solved to determine the optimal strategies for both players of the game. The proposed method in this paper is illustrated with a voting share problem to demonstrate the validity and applicability of the method.